According to a famous article by Max Kleiber*, the scaling of the metabolic rate

Question

According to a famous article by Max Kleiber*, the scaling of the metabolic rate or energy consumption for mammalsPmetab (measured in kcal/day) with the body mass Mb (measured in kilograms) is P metab = 70 Mb0.75 .

*M. Klieber, “Body size and metabolism,” Hilgardia6, 315 (1932)

frequency of respiration (breaths per minute) for mammals obeys the same type of scaling equation as does the specific metabolic rate (i.e. the exponent x is the same, but the constant c is obviously different). What is the ratio of the frequency of respiration of the mouse to that of the cow?

Explanation / Answer

Specific metabolic rate = 70Mb^0.75/Mb

= 70*Mb^-0.25

comparing with cMb^x

x = -0.25

The exponent 0.75 or ¾ is taken for scaling, predicted from the “surface law” of metabolism. According to the surface law, ¾ is the ratio of volume to surface area of an organism. The ratio of volume to surface area is said to affect the rate of heat produced to heat lost to the environment. Kebler adopted the value ¾ rather than 2/3 since the value ¾ is proved to be close to the actual values based on the scaling of circulatory systems and other biological networks.

However, more recent investigations had shown that the b value is close to 2/3 for birds, ¾ for mammals, and 8/9 for reptiles.

A small animal uses more energy per unit body mass, since it has a larger surface area to volume ratio

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